The motion of assemblies of point vortices in a periodic parallelogram can be described by the complex position zj(t) whose time derivative is given by the sum of the complex velocities induced by other vortices and the solid rotation centered at zj . A numerical simulation up to 100 vortices in a square periodic box is performed with various initial conditions, including single and double rows...

A motion of point vortices with periodic boundary conditions is studied by using Weierstrass zeta functions. Scattering and recoupling of a vortex pair by a third vortex becomes remarkable when the vortex density is large. Clustering of vortices with various initial conditions is quantitated by the L function used in point process theory in spatial ecology. It is shown that clustering persists ...

Let ∆ be the ball |x| < 1 in the complex vector space C, let f : ∆ → C be a holomorphic mapping and let M be a positive integer. Assume that the origin 0 = (0, . . . , 0) is an isolated fixed point of both f and the M -th iteration f of f . Then for each factor m of M, the origin is again an isolated fixed point of f and the fixed point index μfm(0) of f m at the origin is well defined, and so ...

For mixing Zd-actions generated by commuting automorphisms of a compact abelian group, we investigate the directional uniformity of the rate of periodic point distribution and mixing. When each of these automorphisms has finite entropy, it is shown that directional mixing and directional convergence of the uniform measure supported on periodic points to Haar measure occurs at a uniform rate ind...

A framework for understanding the geometry of continuous actions of Z was developed by Boyle and Lind using the notion of expansive behavior along lower-dimensional subspaces. For algebraic Z-actions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponents. Here we show that periodic point counts for elements of an entropy rank one action determine the ...

We show that algebraic dynamical systems with entropy rank one have uniformly exponentially many periodic points in all directions.

In this paper, some fixed and periodic point theorems are established in fuzzy cone metric space for generalized contraction mappings and the main theorem is justified by a counter example. 2010 AMS Classification: : 54A40, 03E72

Correspondence: [email protected] Kent State University at Trumbull, Warren, OH 44483, USA Abstract This work is concerned with periodic systems dependent on parameters and investigates differentiability with respect to parameters of the periodic solutions of the systems. Some challenging situations arise from a hyperbolic type of periodic boundary value problem. Using some auxiliary operators and a...

In this paper, a constructive approach for determining CELCS (critical error linear complexity spectrum) for the kerror linear complexity distribution of 2-periodic binary sequences is developed via the sieve method and Games-Chan algorithm. Accordingly, the second descent point (critical point) distribution of the k-error linear complexity for 2-periodic binary sequences is characterized. As a...

In this paper we prove Morse type inequalities for the contractible 1-periodic solutions of time dependent Hamiltonian differential equations on those compact symplectic manifolds M for which the symplectic form and the first Chern class of the tangent bundle vanish over q ( M ) . The proof is based on a version of infinite dimensional Morse theory which is due to Floer. The key point is an ind...